An Algorithmic Approach for Sensitivity Analysis of Perturbed Quasi-Birth-and-Death Processes

Authors:
Quan-Lin Li;Liming Liu
Affiliations:
Department of Industrial Engineering, Tsinghua University, Beijing 100084, P.R. China liquanlin@tsinghua.edu.cn;Department of Industrial Engineering and Engineering Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong liulim@ust.hk
Venue:
Queueing Systems: Theory and Applications
Year:
2004

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Abstract

In this paper, we present an algorithmic approach for sensitivity analysis of stationary and transient performance measures of a perturbed continuous-time level-dependent quasi-birth-and-death (QBD) process with infinitely-many levels. By developing a new LU-type RG-factorization using the censoring technique, we obtain the maximal negative inverse of the infinitesimal generator of the QBD process. The derivatives of the stationary performance measures of the QBD process can then be expressed and computed in terms of the maximal negative inverse, overcoming the computational difficulty arising from the use of group inverses of infinite size in the current literature (see Cao and Chen [11]). We also use a stochastic integral functional to study the transient performance measure of the QBD process and show how to use the algorithmic approach for its sensitivity analysis. As an example, a perturbed MAP/PH/1 queue is also analyzed.